# vector spaces

(1.7 hours to learn)

## Summary

Vector spaces are spaces which are closed under addition and scalar multiplication. Examples include vectors, matrices, polynomials, and functions. Many core concepts of linear algebra, such as linear independence, bases, and dimension, are defined for general vector spaces.

## Context

This concept has the prerequisites:

- vectors (Vectors in R^n are the prototypical example of a vector space.)

## Core resources (read/watch one of the following)

## -Free-

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

## -Paid-

→ Linear Algebra Done Right

A textbook for a second course in linear algebra, with mathematical generalizations of the basic concepts.

Location:
Chapter 1, "Vector spaces," subsections "Definition of vector space" and "Properties of vector space," pages 4-12

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 3.1, "Spaces of vectors," up to "Subspaces," pages 120-121

## See also

-No Additional Notes-